$ SIZE(n^k)$ is defined as the class of problems solvable with Boolean circuits (of fan-in two) with $ O(n^k)$ gates. While $ P/poly$ is defined as those problems over **{0,1}*** which can be solved by an infinite family of polynomial-size circuits $ {Cn}$ .

# Tag: P/poly

## Why isn’t P and P/poly trivially the same?

The definition of P is a language that can be decided by a polynomial time algorithm. The definition of P/poly can be taken to mean a language that can be decided by a polynomial-size circuit (see http://pages.cs.wisc.edu/~jyc/02-810notes/lecture09.pdf). Now, why can’t a polynomial-sized circuit be simulated in polynomial time?